Problem: Solve for $x$ and $y$ using substitution. ${-6x-2y = -12}$ ${y = 5x-2}$
Explanation: Since $y$ has already been solved for, substitute $5x-2$ for $y$ in the first equation. ${-6x - 2}{(5x-2)}{= -12}$ Simplify and solve for $x$ $-6x-10x + 4 = -12$ $-16x+4 = -12$ $-16x+4{-4} = -12{-4}$ $-16x = -16$ $\dfrac{-16x}{{-16}} = \dfrac{-16}{{-16}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {y = 5x-2}\thinspace$ to find $y$ ${y = 5}{(1)}{ - 2}$ $y = 5 - 2$ $y = 3$ You can also plug ${x = 1}$ into $\thinspace {-6x-2y = -12}\thinspace$ and get the same answer for $y$ : ${-6}{(1)}{ - 2y = -12}$ ${y = 3}$